Nīlakantha's planetary models

Journal of Indian Philosophy

Volumn 29, Issue 1-2, 2001, Pages 187-195

  Pingree, David ^a  

^a BROWN UNIVERSITY   (United States)

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[No Author keywords available]

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EID: 52549105284     PISSN: 00221791     EISSN: 15730395     Source Type: Journal    
DOI: 10.1023/a:1017577519011     Document Type: Article

References (26)

1. Jyotirmīmāmsā ed. K.V. Sarma, Panjab University Indological Series 11, Hoshiapur 1977.
2. D. Pingree, Census of the Exact Sciences in Sanskrit, Series A, vols. 1-5, Philadelphia 1971-1994, vol. 3, 175b-177b;
3. D. Pingree, Census of the Exact Sciences in Sanskrit, vol. 4, 142a-142b;
4. and D. Pingree, Census of the Exact Sciences in Sanskrit, vol. 5, 186a.
5. Jyotirmīmāmsā, pp. 27-31.
6. Jyotirmīmāmsā, Ibid., p. 35.
7. Siddhāntadarpana, ed. K.V. Sarma, Panjab University Indological Series 7, Hoshiapur 1976; this edition contains what remains of Nilakantha's own commentary.
8. Tantrasaṅgraha ed. K.V. Sarma, Panjab University Indological Series 10, Hoshiapur 1977; this edition includes the Yuktidīpikā and the Laghuvrtti, both by Śaṅkara, a pupil of Nīlakantha.
9. See D. Pingree, "History of Mathematical Astronomy in India", in C.C. Gillispie, ed., Dictionary of Scientific Biography, vol. 15, New York, 1978, pp. 533-633, esp. pp. 621-623.
10. Siddhāntadarpana 2-7.
11. Pingree, "History" (see note 7), p. 556.
12. The only observations of his own that Nilakantha refers to in the works associated with his new models are used to show that the trepidational motion affects all the fixed stars, not just the ecliptic. These are listed in his Siddhāntadarpanavyākhyā (p. 16): 1. The Moon occulted Citrā when the ahargana of Kali was 1,677,647 (= 12 April 1492). The longitude of the Moon at sunset on 11 April 1492 was 197°, its latitude -2°. Citrā is α Virgo, whose longitude in 1492 was 197;20° and whose latitude was -1;56°. 2. Mercury was north of Citrā when the ahargana was 1,678,524;30 (= sunset of 6 September 1494). The longitude of Mercury was 196;48°, its latitude -1;45°. 3. Rohinī was seen above the Moon when the ahargana was 1,679,003 (= 28 December 1495); the longitude of the Moon at sunset was 64°, its latitude -4°. Rohinī is α Tauri, whose longitude in 1495 was 63;14° and latitude 5;37°. These observations may also have been used in correcting the mean motions of the Moon and the Mercury, but Nīlakantha does not say that they were nor does he describe how they would have been analysed to provide a correction.
13. Pingree, "History", p. 590.
14. Pingree, "HistoryIbid., p. 608.
15. Pingree, "HistoryIbid., p. 623.
16. Pingree, "HistoryIbid., p. 622.
17. Pingree, "HistoryIbid., p. 610.
18. Pingree, "HistoryIbid., p. 623.
19. Pingree, "HistoryIbid., p. 592.
20. K. Ramasubramanian, M.D. Srinivas, and M.S. Sriram, "Modification of the Earlier Indian Planetary Theory by the Kerala Astronomers (c. 1500 A.D.) and the Implied Heliocentric Picture of Planetary Motion", Current Science 66, 1994, 784-790. A seminar on the Tantrasangraha and this interpretation of it was held in Madras on 11-13 March 2000; the proceedings are not yet available.
21. Pingree, "History", p. 558.
22. Pingree, "HistoryIbid., pp. 556, 591, 608, and 609.
23. These verses are rather awkwardly translated by Subramanian et al., "Modification", pp. 788-789.
24. In Siddhāntadarpana 22 and its commentary the grahabhramanavrtta is called the pratimandalam, which is in turn called the jñä tabhogagraha, "(the circle) on which is the planet whose motion is known"; its radius is said to be R (this applies only to the three superior planets). Another circle with equal radius has its circumference touched by a line from the planet to the center (of the earth) at the point where its (geocentric) motion (in longitude) is to be known; this is what Āryabhata called the orbital circle (kaksyāvrtta), the computation of whose radius in yojanas will be described below.
25. The rotations of the śīghrocca of Mercury are given in Siddhāntadarpana 4 as being "on its own circle", i.e., on its grahabhramanavrtta; the same must hold for the motion of Venus' śīghrocca in agreement with Tantrasangraha I 16-18.
26. σ is to 360°. The svavrtta, as Nīlakantha explains in his commentary, still has 360° in its circumference, but its size is smaller.